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N TED STATES IARTMENT OF MMERCE

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NBS TECHNICAL NOTE 529

Determination of

Oxygen Concentration

in Silicon and

Germanium by

Infrared Absorption

U.S.

ARTMENT

OF

OMMERCE

National

Bureau

of

Standards
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NBS TECHNICAL NOTE 529

ISSUED MAY 1970

Nat. Bur. Stand. (U.S.), Tech. Note 529, 21 pages (May 1970)

CODEN: NBTNA

Determination of Oxygen Concentration

in Silicon and Germanium

by Infrared Absorption

W. R. Thurber

Electronic Technology Division

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C, 20402.

(Order by SD Catalog No. CI 3.46:529). Price 30 cents.

Determination of Oxygen Concentration in Silicon and Germanium

by Infrared Absorption

W. R. Thurber

Infrared absorption measurements were made at room temperature, 80 K, and 20 K to determine the absorption coefficient

of oxygen in silicon and germanium single crystals. A study

was done to compare the results of four experimental methods

,

which involved both absolute and difference procedures.

Sources of error were identified, including that due to calculating the absorption coefficient with an approximate equation

which neglects multiple internal reflections. Measurements

made on the same specimen at several temperatures give additional data on the relation of oxygen concentration to absorption coefficient at low temperatures.

Key Words: absorption coefficient; infrared absorption; germanium; methods of measurement; oxygen in germanium; oxygen in

silicon; silicon

1. INTRODUCTION

This report summarizes results on the oxygen concentration of silicon and germanium single crystals determined by infrared absorption measurements at room temperature, 80 K, and 20 K. An important part of the

report is an experimental comparison of absorption measurements made by

various methods on silicon slices. The procedures followed in making the

absorption measurements were essentially the same as those given in various ASTM documents [1].

,,. The instrument used for most of the work was a Perkin-Elmer Model

337 double beam, infrared grating spectophotometer , linear in wavelength

with adjustable slit width. A scale expansion accessory added to this

instrument was available for most of the measurements. Also a slower

scan motor (72 min to cover the range 7.5 to 25 urn) was installed for re- cording narrow absorption bands. Occasionally spectra were run on other

instruments at NBS for comparison with those obtained on this spectrophotometer.

The commercial instrument is identified in this paper in order to

specify adequately the experimental procedure. In no case does such

identification imply recommendation or endorsement by the National

Bureau of Standards, nor does it imply that the equipment identified

is necessarily the best available for the purpose.
Figure 1,

OD COPPER SEAL

8Dmm OD

2 FLANGED OPENINGS 80° APART- GROUND FLAT

Dewar system used in sample beam of spectrophotometer. A photograph of the germanium specimen (S) mounted on a copper plate (P) attached to a flange (F) at the end (E) of the inner tlask is shown in the inset. A thermocouple (T) is bonded to the side of the specimen.
The absorption coefficient of oxygen increases with a decrease in

temperature , so smaller concentrations of the impurity can be detected

when the specimens are cooled. Double Dewar flasks were used to cool

both the sample and reference specimens to temperatures of 80 K (liquid

nitrogen) and 20 K (liquid helium in the inner flask).

The Dewar system for the sample beam shown in Fig. 1 is patterned

after an optical cell designed by H. N. Hersh [2]. The Dewar system for

the reference beam was similar but smaller in diameter to fit the available space in the spectrophotometer. Potassium bromide windows, 5-mm

thick, were secured to the flanged openings with a varnish which provided

the necessary vacuum seal. The specimens were mounted on copper plates

with the aid of spring clips and conductive silver paste. This assured

good thermal contact in order to dissipate heat from the specimen due to

the incident radiation and the room temperature environment . As shown in

the inset in Fig. 1, the plate was fastened to a flange soldered onto the

copper seal at the end of the inner flask. The alignment was such that

the hole in the plate through which the radiation passed was in the center of the Dewar windows. It was found that if the flask were positioned

so that the copper plate faced the incoming radiation, then lower temperatures were reached than when the specimen faced the incident beam.

This was attributed to the more direct path provided by the copper plate

in conducting heat to the liquid helium. A thermocouple was glued to the

side of the specimen (silver paste was used at the junction for better

thermal contact) and the leads emerged from the Dewar system through the

joint at the top of the inner flask.

2. EXPERIMENTAL PROCEDURES

There are several procedures by which the absorption coefficient due

to an impurity in a crystal can be determined. All of the four methods

investigated in this study should yield the same value for the absorption

coefficient if the measurements are carefully done, the instrument is

functioning properly, the correct equation is used, and the proper cor- rection is made for lattice absorption.

The absolute transmittance method follows the procedure given in

ASTM Method FM-5-64T [1]. The spectrophotometer is initially adjusted so that 100 percent transmittance is read with air in both beams and percent is recorded with the sample beam blocked. Then the specimen, with

polished, parallel faces, is placed in the sample beam and the spectrum

recorded. An example is shown in Fig. 2a. The minimum percent transmittance T is noted for the 9-um band and the absorption coefficient is

determined by computations involving the transmission equation which is

discussed in Section 3. For all but the most accurate work, a graph in

the ASTM method can be used in lieu of the computations . The oxygen con- centration is obtained from a calibration curve in the document. This

procedure has the disadvantage that the absolute transmittance is used

which requires correct and 100 percent transmittance readings and ne- cessitates good preparation of the specimen surfaces to keep scattered

light to a minimum. Any surface films which affect the reflectivity will

introduce errors. Also the specimen resistivity must be greater than

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1 ft-cm; otherwise free carrier absorption will reduce the transmittance

In the air reference method, the spectrum is also obtained with air

in the reference beam of the spectrophotometer and then a straight baseline is drawn tangent to the peaks in transmittance on each side of the

9-um absorption. In the example shown in Fig. 2b an attenuator was used

in the reference beam to move the trace higher on the transmittance scale

and thereby magnify the recording. The total absorption coefficient is

calculated from the equation

T = T e" a

' x

, n

. m o (1)

where

T = transmittance minimum for the impurity absorption peak,

m

T = baseline transmittance measured at the same wavelength as o m

a' = absorption coefficient, and

x = thickness of slice.

To obtain the absorption coefficient due to oxygen, a lattice contribution is subtracted from the total coefficient.

In the single-beam difference method (or reference standard method

[3]) the test specimen and an oxygen-free crystal of the same thickness

and surface finish are consecutively recorded on the same paper as shown

in Fig. 2c. In Eq. (1), which is used for the calculations, T is the

relative transmittance of the specimen at the impurity absorption peak

and T is the transmittance of the oxygen-free reference slice at the

same wavelength. The absorption coefficient a' is that due to oxygen only

as using a reference crystal to obtain T eliminates the lattice absorption.

In the double-beam difference procedure, the spectrum is obtained

with the test specimen in the sample beam and an oxygen-free slice of

the same thickness in the reference beam. As illustrated by Fig. 2d,

this method cancels out the lattice absorption. The baseline T is drawn

as a straight line coincident with the transmittance trace on both sides

of the absorption band. The flat baseline allows the trace to be made

near the top of the transmittance scale, thereby giving a peak size which

is larger than that obtainable by the other methods . Differences in free

carrier absorption between the two slices will give an irregular or sloping baseline, but will have little effect on the impurity peak. Equation

(1) is used to find the absorption coefficient due to oxygen. This diff- erence procedure is generally the most accurate method, especially for

small impurity concentrations , and may be the only one with the required

sensitivity.
Table 1. Results of measurements of the absorption coefficient of oxygen in silicon specimens by

different methods

Crystal Specimen

thickness

Absolute Ai ar reference

Std. dev. a

Singl

a'

e beam di Std. dev.fference

a

Doubl

a'

e beam di Std. dev.

fference

number

a Std. dev. a

cm cm

-1 cm" 1 cm

-1 cm

-1 cm" 1 cm" 1 cm

-1

R818A 0.1036 2.03 0.08 2.21 0.04 2.22 2.38 0.03 2.10 2.69 0.06 2.39

.201 2.08 .16 1.99 .05 2. 09 2.12 .02 1.94 2.44 .12 2.24

.500 2.38 .15 2.09 .09 2.31 2.29 .09 2.22 2.39 .07 2.32

L42Mx .1037 1.24 .03 1.33 .03 1.43 1.45 .06 1.27 1.63 .03 1.43

.201 1.35 .19 1.29 .04 1.44 1.41 .03 1.27 1.61 .11 1.46

.500 1.39 .04 1.16 .02 1.40 1.35 .02 1.29 1.46 .04 1.40

1105 .177 1.21 .07 1.15 .05 1.30 1.23 .01 1.10 1.47 .05 1.32

1174 .201 1.15 .10 1.12 .07 1.28 1.31 .06 1.18 1.40 .04 1.26

602826 .185 3.65 .12 3.42 .16 3.43 3.60 .14 3.33 3.96 .03 3.68

a' is the oxygen absorption coefficient calculated from the approximate equation T = T e"

a

.

a is the oxygen absorption coefficient calculated using the complete transmission equation and includes

corrections discussed in the text.

Table 2. Ratio of oxygen absorption coefficient at about 80 K to that at room temperature and oxygen concentration for silicon specimens

Specimen Temperature a80 Temperature a 300 a80/

a300 Oxygen

K cm

-1

K cm" 1 atoms/cm 3

21-157-4-2 79 0.806 308 0.383 2.1 1.84 x 10 17

1174 80 3.03 308 1.26 2.4 6.05

reference [7] 78 3.4 297 1.8 1.9

C 8.6

reference [4] 90 4.4 room 2.6 1.7 12.5

Calibration equation: oxygen atoms/cm 3 = 4.8 x io 17

a

Background absorption was estimated.

Ratio 2.1 when slit width correction applied.

SI it width not given.

300

-
3. COMPARISON OF METHODS FOR SILICON

Absorption measurements were made on several silicon specimens using

each of the four methods given in Section 2. The results are given in

Table 1. Each value listed is the average of about five recordings of

the absorption band and an estimated standard deviation of the mean was calculated from the individual measurements . Also listed are the values

after corrections were made for the known errors in the last three methods. Two corrections are necessary. The first involves the error introduced when the approximate equation, Eq. (1), which neglects multiple internal reflections, is used instead of the more complete equation

I. (1-R) 2 e"ax

I = i (2)

l_ R

2 e -2ax

where I = transmitted intensity measured at wavelength of impurity

absorption peak,

I. = radiation intensity on specimen at normal incidence,

R = reflectivity of a single air-crystal interface,

a = absorption coefficient, and

x = thickness of slice.

The calculations relating the absorption coefficient a determined by Eq.

(2) with the a' of Eq. (l) for both air reference and difference methods

are outlined in the appendixes. To determine when Eq. (l) can be used

without appreciable error (10 %), calculations were made for a range of

oxygen absorption coefficients and specimen thicknesses using constants

appropriate for germanium and silicon. Graphs of the results are given in

the appendixes

The second correction applies only to the air reference method and

involves the baseline intensity which is used in the approximate equation. The baseline tangent to the peaks in transmittance on each side of

the oxygen band does not place all of the lattice absorption (0.8 cm

-1

) under the baseline, but only that amount in the lattice peak. From the

work of Kaiser, Keck, and Lange [4], it is evident that the excluded

lattice absorption is about half of the total value. Thus it would be more appropriate to subtract 0.4 cm

-1

, instead of . 8 cm

-1

, when determining the oxygen absorption coefficient by the air reference method.

Consequently 0.4 cm

-1 was added to each of the absorption coefficients in

the corrected column for the air reference measurements.

The corrected absorption coefficients as determined by the four

methods (Table 1) are in reasonable agreement. If 0.4 cm

-1 had not been

added to each of the air reference values, all of these would be much

smaller than those obtained from the other methods. Other trends are:

(1) The double-beam difference method always gives a larger coefficient

than the single-beam difference method, and (2) for the absolute transmittance method the absorption coefficient varies systematically with

specimen thickness, with thicker specimens in better agreement with the

7
other methods . The latter trend is not unexpected as the various errors

(such as and 100 percent transmittance settings and surface preparation) are relatively more important for a thin specimen than for a thick

one

.

Another source of error in the measurements was the non-linearity of

the spectrophotometer as a function of baseline transmittance. This

error is most readily observed in the double-beam difference method by

running the specimens at a high transmittance baseline and then repeating

the scan at a lower transmittance baseline (achieved by adjusting the 100

percent control). Consistently, it was found that the absorption coefficient determined from a baseline of 70 to 80 percent transmittance was several percent smaller than that claculated from a 90 to 100 percent

baseline. This result may not be typical as the effect was somewhat

smaller on another instrument of similar design.

Another factor which may affect the results is the spectral slit

width of the spectrophotometer and its relation to the full width at half

maximum intensity (FWHM) of the impurity peak. The spectral slit width

is the mechanical width of either the exit or the entrance slit, whichever is the larger, divided by the linear dispersion in the exit slit

plane. The spectral slit width must be narrow enough so that the full

peak height will be reproduced. The oxygen absorption band in silicon

has a Gaussian profile at room temperature with a wide FWHM so that the

slit setting of the instrument is not critical. The FWHM observed in

this work was 35 cm

-1 and values quoted in the literature are 30 cm

-1

[5] and 32 cm

-1 [6]. The FWHM determined from the spectra of Hrostowski

and Kaiser [7] was about 32 cm" . The appropriate ASTM document gives

32 cm

-1

. At 80 K the oxygen band is narrow so correspondingly narrow

instrument slit widths must be used. The FWHM at 80 K found in this work

was 20 cm" 1 and values from the literature are also about 20 cm" 1 [4,7].

The ASTM value for 80 K is likewise 20 cm" 1

.

When recording sharp absorption bands with narrow slit widths , it

is important to scan the wavelength range of interest at a slow speed.

Otherwise the peak height will be attenuated or, with a fast pen response, overshoot may occur due to the rapid change of absorption. A

slow scan speed will improve the signal to noise ratio as the pen re- sponse can be reduced without loss of detail. The reproducibility of the

peak shape is a useful criterion in determining the quality of the re- cording. When the peak is narrow, abscissa expansion is necessary to determine its shape and FWHM. The expansion was achieved by using an ex- ternal recorder in conjunction with the 72 min scan speed of the spectrophotometer. Ordinate expansion was also used when the peak height was small

.

4. OXYGEN CONCENTRATION AND TEMPERATURE DEPENDENCE

OF ABSORPTION COEFFICIENT FOR SILICON

Recent measurements [8] on the relation between absorption coefficient and oxygen concentration are in disagreement with the earlier work

of Kaiser and Keck [9], which serves as the calibration for ASTM method
F-45 . The new equation relating oxygen content to the absorption coefficient at 9 urn [oxygen atoms/cm 3 = 4.8 x 10 17 a (cm-1

)] gives about twice

the oxygen that is obtained by use of Kaiser and Keek's results. Infrared absorption measurements and the lithium precipitation method [10]

give the same amount of oxygen in silicon crystals if the new calibration

is used for the infrared work. Also the oxygen content in silicon as determined by 3 He activitation [11] was about twice that found by infrared

absorption. The calibration equation used for the absorption analysis

was not given, but the Kaiser and Keck relation was probably used as it

has been the customary one . The use of the new calibration would bring

the oxygen content as determined by absorption into close agreement with

that found by 3 He activation

As mentioned in the introduction, the height of the absorption peak

increases with a decrease in temperature. At room temperature the absorption appears as a single peak, but when the specimen is cooled two

peaks emerge which are well resolved at 80 K [7]. At 20 K, the peak

which was the stronger of the two at 80 K is now the weaker one . The

stronger absorption peak at 18 K has a coefficient about three times as large as that of the broad peak at 297 K [7]. On the one specimen measured at 20 K in the present work , a value of about 5 was found for the

ratio a /a . Pajot [5] measured specimens cooled to 8 K using a narrow spectral slit width (0.32 cm

-1

) and found that a /a was about

25. Since the absorption coefficient is this strong at liquid helium

temperatures , it is possible to determine oxygen concentrations down to

about 1 x 10 1 atoms/cm3

. The disadvantages of the procedure are the narrow slit width required to obtain the full peak height and the low

temperature which must be consistently achieved.

Measurements at 80 K are of special interest as the ASTM Method

F121-70T includes a calibration for this temperature. Table 2 lists absorption coefficients obtained at temperatures near 80 K and 300 K and

the ratio calculated from the coefficients. Also included is the oxygen

concentration for each specimen based on the coefficient at 300 K. For

the literature references the data were taken from the published graphs,

and the background absorption for an oxygen-free slice was subtracted to

get only the absorption coefficient due to oxygen. The double-beam difference method was used for the present measurements at room temperature

and at 80 K. A gold-cobalt versus chromel thermocouple was used to determine the temperature. The value of 30 8 K given for nominal room temperature measurements was the temperature obtained by attaching a thermocouple directly to one of the specimens. Thus the heating of the specimens by the infrared beam can give some error if the calibration is based

on results at 300 K. The work of Hrostowski and Kaiser [7] can be ex- trapolated above 300 K to get an approximate idea of the change in absorption coefficient with temperature. It is fortunate that a varies

slowly with temperature so that heating of the specimens will not be a major source of error.

Hrostowski and Kaiser state that their absorption coefficients have

a maximum error of 10 percent in regions of strong absorption because of

the slit widths which were used in recording the narrow bands. Since at

9
room temperature the band is wide, the error occurs only for 80 K measurements and a correction of 10 percent in the ratio a

8c/

a

30£)

of Table 2 increases it to 2.1. The slit width used in the present work was sufficiently narrow so that any corrections would be only a few percent. The

absorption coefficient calculations were made with Eq. (2) using 0.4 cm

-1

for the lattice absorption coefficient at 80 K and 0.2964 for the reflectivity.

On the basis of this work and various ASTM round robins, it appears

that ±20 percent is a realistic figure to expect for the multi -laboratory

precision for determination of oxygen in silicon by infrared absorption.

5. MEASUREMENTS ON GERMANIUM

Procedures similar to those described for silicon may be used for

measurements on germanium. There is some disagreement on the calibration

equation relating the absorption coefficient of the 11.7-um band to the

interstitial oxygen concentration. Kaiser and Thurmond [12] used vacuum

fusion determinations made with an iron bath to calibrate their infrared

absorption measurements and found that oxygen atoms /cm 3 = 0.5 x 10 17 a (cm-1

). Millett, Wood, and Bew [13] repeated the work and obtained inconsistent results with an iron bath. However, when they used a platinum

bath their data was consistent to about 20 percent of the total oxygen

content. The calibration found was that oxygen atoms/cm 3 = 1.25 x 10 17 a (cm-1

). This is the same factor that Bloem, Haas, and Penning [14] derived, but this is coincidental, as they based their calculation on silicon data which is now considered inaccurate. Fox [15] determined the

oxygen content of germanium by the lithium precipitation technique and

compared the results with infrared absorption measurements on specimens

cooled to 20 K. The calibration obtained was that oxygen atoms /cm3 = 3.1

x 10 16 a (cm-1

). This is in good agreement with the results of Millett,

et al. , as data on the variation of the absorption coefficient with temperature show that the coefficient is about four times larger at 20 K than

at 300 K.

The free carrier absorption coefficient per unit carrier concentration is about ten times higher in p-type than in ft- type germanium [16].

The absorption cross section in p-type material is 7 x 10 -1 ° cm at 11.7

ym for both 300 and 80 K [16-18], and the absorption coefficient is the

product of the cross section and the carrier concentration. The data

from measurements on many specimens at room temperature, 80 K, and 20 K

were analyzed to compare the expected values for the background absorption coefficient with the experimental ones. The coefficients varied

from 0.07 to 0.15 cm

-1

, independent of temperature, for p-type specimens

with carrier concentrations in the range 4 x 10 13 to 2 x 10^ cm

-3

. The

correction for multiple reflections is fairly insensitive to the value

used for the background absorption coefficient, so 0.1 cm

-1 was used for

the specimens included in this report as they all had carrier concentrations below 2 x io lt+ cm

-3

. This is also the value used by Kaiser and

Thurmond [12] for room temperature measurements on a specimen with low

carrier density.

10
Table 3. Absorption coefficient and FWHM as a function of temperature for

the 11.7 pm oxygen band in germanium specimen NBS-91 (thickness 1.19 cm)

Temp.

Spectral

Slit width a

' Std. dev. R a FWHM

Peak area (a-FWHM)

K cm" 1 cm

-1 cm-1 cm

-1 cm

-2

305 3.5 0.0081 0.0006 0.360 0.0066 4.7 0.031

229 3.5 .012 .002 .358 .0097 4.7 .046

153 3.5 .017 .002 .356 .014 3.6 .050

81 3.5 .027 .002 .354 .022 3.5 .077

81 2.5 .028 .005 .354 .023 2.8 .064

23 3.5 .030 .002 .352 .025 2.8 .070

23 2.5 .039 .003 .352 .032 2.6 .083

Table 3 lists measurements at several temperatures of the absorption coefficient and FWHM of the oxygen band in specimen NBS-91. The

double-beam difference method was used and the calculations were corrected to include the effects of multiple internal reflections. The absorption coefficient obtained at 23 K with the narrow slit width is significantly larger than the one found using the wider slit. The area un- der the absorption band increases with a decrease in temperature. The

FWHM at room temperature may be concentration dependent as measurements

on several specimens indicated that the FWHM increased as the oxygen

concentration increased. The literature references give values for FWHM

of 5 cm

-1 [14] and 6 cm

-1 [19], whereas the appropriate ASTM document

lists 8 cm

-1 [1]. Bloem, Haas, and Penning [14] give 3 cm-1 for the FWHM

at 77 K, and a value of 2.8 cm

-1 is obtained from the work of Kaiser

[19]. At 5 K a value of 2.5 cm

-1 is determined from spectra of Kaiser.

All of the low temperature FWHM, including those in Table 3, may be

slightly greater than the true ones because of the relatively wide slit

widths used.

Table 4 gives the temperature variation of the absorption coefficient of the 11.7 urn oxygen band. Literature values, in addition to the

data obtained in this work, are included. Room temperature was estimated

as 305 K to include heating by the infrared beam. The low temperature

values were calculated from thermocouple readings for each specimen. All

measurements were made by the double-beam difference method and were

11
Table 4. Temperature dependence of the absorption coefficient of oxygen in germanium specimens

Specimen Thickness

Room

T temperature

a Liquid

T

ni troqen

a Liquid

T helium

a a80 ^0

a20

u 300

cm K cm-1 K cm" 1 K cm- 1

NBS-01 0.844 305 0.015 80 0.028 24 0.040 1.9 2.7

NBS-23 1.18 305 0.0095 79 0.025 12 0.033 2.6 3.5

NBS-24 1.19 305 0.0071 78 0.018 12 0.025 2.5 3.5

NBS-91 1.19 305 0.0066 81 0.023 23 0.032 3.5 4.8

NBS-101 1.09 305 0.11 81 0.26 47 0.33 2.4 3.0

Reference[14] 300 0.38 77 1.0 2.6

Reference'[19] 300 5.9 77 12.9 5 14.2 2.2 2.4

Table 5. Oxygen content of germanium crystals as determined by infrared absorption measurements on specimens at room temperature and at about 20 K

Crystal 300 K - difference method 20 K - air reference method 20 K - difference method

number a Std. dev Oxygen a Std. dev. Oxygen a Std. dev. Oxygen

cm

-1 atoms /cm 3 cm" atoms/cm 3 -1 cm atoms/cm 3

NBS-01 0.015 0.002 19 x 10 11* 0.058 0.006 18 x 10 11* 0.040 .0.004 12 x 10 11*

NBS-02 .0083 .0018 2.6

NBS-23 .0095 .0017 .033 .003 10

NBS-24 .0071 .0009 8.9 .036 .004 11 .025 .002 7.7

NBS-71 .0045 .0007 1.4

NBS-91 .0066 .0005 8.3 .033 .004 10 .032 .002 9.9

NBS-101 .113 .003 141 .35 .01 108 .33 .01 100

NBS-613 .0071 .0009 2.2

12
corrected for multiple internal reflections. The ratios for specimen

NBS-91 are noticeably larger than those for the other specimens, but no explanation can be given.

Table 5 lists the absorption coefficient and oxygen content of germanium crystals as determined from infrared absorption measurements by

the double-beam difference method at about 300 K and by the difference

and air reference methods at about 20 K. All of the absorption coefficients have been corrected for multiple internal reflections. Each reported value is the average of 5 to 10 recordings of the absorption band

and an estimated standard deviation of the mean was calculated from the

individual measurements . There is probably additional systematic error

as evidenced by disagreements between the results of the air reference

and difference methods on the same specimen at the same temperature. A

flat baseline occurs in the difference measurements and this reduces the

error involved in sketching the steep baseline corresponding to an oxygenfree crystal, which is required to analyze the data with air in the reference beam. The oxygen concentrations at 300 K were obtained using the

calibration of Millet, et al. For 20 K measurements the work of Fox was

used to relate oxygen content to absorption coefficient.

A minimum absorption coefficient of about 0.003 cm

-1 can be detected

in a 1-cm thick specimen using the double-beam difference method with ordinate scale expansion. Of course, the accuracy is poor for coefficients

this small. At 20 K, an absorption coefficient of 0.003 cm

-1 corresponds

to an oxygen concentration of just under 1 x 10 1 atoms/cm .

The oxygen content of most of the specimens listed in Table 5 has

been determined by lithium precipitation and by lithium ion mobility.

These results will be discussed and compared with the infrared absorption

measurements in a forthcoming NBS Technical Note.

ACKNOWLEDGEMENTS

Some of the data presented were obtained on round robin specimens

circulated by Subcommittee IV of ASTM Committee F-l on Materials for Electron Devices and Microelectronics. The support of the Arms Control and

Disarmament Agency and the AEC Division of Biology and Medicine for portions of the germanium work is gratefully acknowledged.

13
References

1. "Tentative Method of Test for Oxygen Content of Silicon," (ASTM Designation: F45-64T) 1969 Book of ASTM Standards, Part 8; "Recommended Practices for Infrared Absorption Analysis of Impurities in Single

Crystal Semiconductor Materials," "Method of Test for Interstitial

Atomic Oxygen Content of Silicon by Infrared Absorption," and "Method

of Test for Interstitial Atomic Oxygen Content of Germanium by Infrared Absorption" (ASTM Designations: F120-70T, F121-70T, and F122-70T

respectively) to appear in 1970 Book of ASTM Standards, Part 8.

2. H.N. Hersh, "Color Centers in X-rayed Potassium Iodide," Phys. Rev.

105 , 1158-1167 (1957).

3. "Recommended Practices for General Techniques of Infrared Quantitative Analysis," (ASTM Designation: E168-67) 1969 Book of ASTM Standards, Part 30.

4. W. Kaiser, P. H. Keck, and C. F. Lange , "Infrared Absorption and

Oxygen Content in Silicon and Germanium," Phys. Rev. 101 , 1264-126 8 (1956).

5. B. Pajot, "Improvement in the Detection of Oxygen in Silicon by

Infra-red Absorption," Solid-State Electron. 12_, 923-925 (1969).

6. A. Smakula and J. Kalnajs, "Oxygen Impurity in Silicon Single Crystals," J. Phys. Chem. Solids 6_, 46-50 (1958).

7. H. J. Hrostowski and R. H. Kaiser, "Infrared Absorption of Oxygen in

Silicon," Phys. Rev. 107 , 966-972 (1957).

8. J. A. Baker, to be published in Solid State Electronics.

9. W. Kaiser and P. H. Keck, "Oxygen Content of Silicon Single Crystals," J. Appl. Phys. 2J3, 882-887 (1957).

10. M. I. Iglitsyn, G. P. Kekelidze, and G. V. Lazareva, "Determination

of the Amount of Oxygen in Silicon by the Lithium Diffusion Method,"

Fiz. Tver. Tela 6_, 3148-3150 (1964) [Trans. Soviet Physics - Solid

State 6_, 2508-2509 (1965)].

11. G. I. Aleksandrova, A. M. Demidov, G. A. Kotel'nikov, G. P.

Plashakova, G. V. Suknov, D. Ya. Choporov, and G. I. Shmanenkova,

"Determination of Oxygen Content in Germanium and Silicon by Activation with He 3 Ions," Atomnaya Energiya 23, 106-109 (1967) [Trans.

Soviet Atomic Energy 23_, 797-801 (1967)17

12. W. Kaiser and C. D. Thurmond, "Solubility of Oxygen in Germanium,"

J. Appl. Phys. 32, 115-118 (1961).

14
13. E. J. Millett, L. S. Wood, and G. Bew, "Oxygen in Germanium by

Vacuum Fusion and Infra-red Absorption," Brit. J. Appl. Phys. 16_,

1593-1594 (1965).

14. J. Bloem, C. Haas, and P. Penning, "Properties of Oxygen in Germanium," J. Phys. Chem. Solids 12, 22-27 (1959).

15. R. J. Fox, "Lithium Drift Rates and Oxygen Contamination in Germanium," IEEE Trans. Nual. Soi. NS-13 , 367-369 (1966).

16. W. Kaiser, R. J. Collins, and H. Y. Fan, "Infrared Absorption in

P-Type Germanium," Phys. Rev. 91, 1380-1381 (1953).

17. H. B. Briggs and R. C. Fletcher, "Absorption of Infrared Light by

Free Carriers in Germanium," Phys. Rev. 9_1, 1342-1346 (1953).

18. A. H. Kahn, "Theory of the Infrared Absorption of Carriers in Germanium and Silicon," Phys. Rev. 97_, 1647-1652 (1955).

19. W. Kaiser, "Electrical and Optical Investigations of the Donor Formation in Oxygen-Doped Germanium," J. Phys. Chem. Solids 2_3, 255-260

(1962).

15
APPENDIX A

CALCULATION AND GRAPHS RELATING THE IMPURITY ABSORPTION COEFFICIENT OBTAINED BY THE APPROXIMATE EQUATION TO THAT FOUND FROM THE COMPLETE EQUATION FOR THE DIFFERENCE METHODS

The impurity absorption coefficient is determined by calculations involving the ratio of

the transmittance at the impurity peak (T ) to the transmittance at the same wavelength for no impurity absorption (T ). The intensity in the sample beam of the spectrophotometer at the impurity peak is

KI.(l-R) 2 e _a

t x

I !_ R

2 e -2a

t x

with the total absorption coefficient a = a. + a , where a. is the impurity absorption co- efficient and cl is the background coefficient which includes lattice and free carrier absorption. The constnat K represents an attenuation of the sample beam which is achieved by

adjusting the 100 % control. The intensity in the reference beam which contains an impurity

free specimen is

I =

X I.(l-R)2 e -V

1-R2 e-2 V

The minimum transmittance at the impurity peak is

I , -2a, x

s „ -a.x 1-R^e °

T = -=r- = Ke 1 m Z i r>2 ~2a x

r 1-R e t

The baseline transmittance is T =

I sr a.=0

i

= K

T o -2 <* x

Thus m -a.x l-R2 e b

e i T o -2a.x

1-R2 e t o

—U . X When the approximate equation is used, an af is obtained from T^/^ - e i

Equating the above two equations, the solution obtained for a' in terms of a. and the other

parameters is

In the limit of small a.x the above equation can be written as

a. - a.

i i a.

i

2R2 e' 2a

hx

a

i x"*° l-R2e"2V

Thus the percent error is independent of a. when a. is small as clearly shown in the graphs

which follow. In the limit of small (a. +

1

a, ) x, the quantity (af - a.) /a. approaches

2R2 /(1-R2 ), a limit dependent only on tne reflectivity value. For semiconductors with a high reflectivity, such as germanium, this factor is large and corrections are needed when

the approximate equation is used for calculations

.

16
c P

o (1) rd •H CD P P £1 0) G

ft P 5 O

Ph o

o e Td •H

CO CD H

A & CO •H

rd Mh 3 CO ^x) CO G P (3 -p H

•H 3 C

& o rd T3 3 Mh P G

a CO rd E p G X)

•rH rd o ^ o G

CD P CD rC CD W3 P T3) Eh £

C rd O

CD

CD c • E

5 O X 3. P «H 1 CD P CO CD rQ (0 CO 3 CD CD CD CJ1 G rG O <D X P

C o

CD CD •H P ^ O ,G O

CD C +j 4h

Mh rd <P P a CD •H CD P

nd -H E rd e H •H P co o P

c c CD ft

(D rd ft O

o p. CO p

p. p ft

<D ip ft

a, a; o rd p

CD 0) CO CD ,C H CD P P1 ft 3 rd E H

Mh O rd ,G O o > H

co cd H rG

T3 rC rd S

O -H P

,C CD #» P M >-H

CU C CD 1 E -H CO E w o

0) 3 P.O CO C TJ Mh • CU (1) o

& c G

CD 'H II Mh E •H

Mh P p rQ •H CD rd d

T3 +J G

CD crnd

0) X3 CD g

,£ rd P P CD G P m

P CD rd en -H E CD Mh O •H CM •H X • • ,g Mh O o X

ft Mh P. rd (D ft II o

p. o ft o

CD O rd Pi CO

CO

CD3

hO •H

ft
ro E c 3 o Qv •H •H CU p c P JC CU rd (X P 5 E P k o e T3 0) w o CU M

,QU

w

rd uh 3 C

•rH ^0 w P c p Tj •H 3 c c ^ O rd rd 3 Uh -p XI a w £ P C C

•H rd o Q)

4=1 o bO

d) P

4=: <1J ^ P T3 ,C O C H C rd E

0) 3.

<d

q • 1 S o X c- P -H • <U P w H A n3 W <H 3 0)

cu cr c CU O CU x. X

a. o P

0) 0) •H u o ~ P

0> c P o

U-n rd tp <P P c

•H P 0) T3 -H E P e •H rd P w o •P G C a) P

CU 03 ft ft O u CO o k P p

CU >p

a

a <u o a p rd

a; cu

W

X

H o; 0)

p

a 3 P e H rd Mh rd o o > O w cu H •H

x) ,c rd JZ O P P. £

4=! a> P bO > ft a) c Q)r-> g -H V) 1 W E

<u

d

u o o o

P. XI 4h

H

0) cu • ^ c C O

d) -HO

tp e •H II Un p. P

•P <D rd rQ

x)

p 3 &

<D a*

CU X) Q) Tj X C P P <u rd c -p P a> rd O • O -P E ID ^

Mh

O •H CO •H X • o

rC IP o o o

OhMh

u CO

cu a) Cu II p a,

p

u o rd Pi rd

001

x 7

cup.

•H
APPENDIX B

CALCULATION AND GRAPH RELATING THE IMPURITY ABSORPTION COEFFICIENT OBTAINED BY THE APPROXIMATE EQUATION TO THAT FOUND FROM THE COMPLETE EQUATION FOR THE AIR REFERENCE METHOD

The impurity absorption coefficient is determined by calculations involving the ratio of

the transmittance at the impurity peak (T ) to the transmittance at the same wavelength for

no specimen absorption (T ). The intensify in the sample beam of the spectrophotometer at

the impurity peak is

I

-a x

I. (1-R) 2 e t

1 !_R2 e

"2 V

with a = a. + a , where a. is the impurity absorption coefficient and o^ is the background

coefficient^which includes

1 lattice and free carrier absorption. The intensity in the reference beam with only air is

I = K I. r 1 where the constant K represents at attenuator in the reference beam. The minimum transmittance at the impurity peak is

^s_ _ (1-R) : m I K (1-R2 e~"0

Assume that the baseline is drawn to coincide with the transmittance for no specimen absorption (only reflectivity losses); then

I

o I r

(1-R) 2

-ax (1-R2

) Thus — = e o

a

t

=

° K (1-R2

) \ -a

tx (1-R2 To

" S l-R2 e- 2at*

-a'x

When the approximate equation is used, an a^ is obtained from T^/^ = e t

Equating the above two equations, the solution obtained for a^ in terms of a

t and the other

parameters is

a' = a^ + In

t t x

/ , -2a x

1 , / 1-R2 e t 1-R'

Using the relations that a^ = «: + «b

and c^. = a

± + o^ , it is possible to write the above

equation as

re' - re / ? ~2(a. + an )x \ a

i a

i 1 . / 1-R2 e i b _ . a.

l 1-R'

It is clear from this equation and the graph on the next page that the approximate equation

should not be used unless the impurity absorption is larger than any competing background

absorption regardless of the value of the reflectivity. Providing there is no competing absorption (a. = 0), the approximate equation can be used with the air reference method when

a x is small, as the correction factor is simply 2R2 /(1-R2 ), which is the limit found in the

same situation for the difference methods. It is well to remember that this factor is significant when R is large. For silicon with R = 0.30, it is a 20 percent correction. In the

limit of large a.x no correction is needed of course.

19
.0 2.0

a] in cm"1

Figure 5. Graph for the air reference method of the percent difference

between the impurity absorption coefficient determined using

the complete transmittance equation and that found from the

approximate equation for several values of specimen thickness

x. The constants used were R = 0.2995 and a = 0.8 cm

-1

, which are appropriate for the 9-ym oxygen band in silicon at

300 K. 20

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